Voozh

A332620

a(n) = Sum_{k=1..n} n^(n/gcd(n, k)).

1, 6, 57, 532, 12505, 93786, 4941265, 67117128, 2324524401, 40000400110, 2853116706121, 35664407810076, 3634501279107049, 66672041585829330, 3503151123049919265, 147573952606856413456, 13235844190181388226849, 236078448452969449231206, 35611553801885644604231641

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..385

FORMULA

a(n) = [x^n] Sum_{k>=1} Sum_{j>=1} phi(j) * n^j * x^(k*j).

a(n) = Sum_{k=1..n} n^(lcm(n, k)/k).

a(n) = Sum_{d|n} phi(d) * n^d.

a(n) = n * A332621(n).

MATHEMATICA

Table[Sum[n^(n/GCD[n, k]), {k, 1, n}], {n, 1, 19}]